Review System Property State Process Cycle Zeroth Law

Example 2-4

Applied Thermodynamics Thermodynamics: Energy, Work, Power and Heat

Energy Forms of Energy –Kinetic: KE = ½ mv 2 –Potential: PE = mgh Specific energy: –ke = ½ v 2 –pe = gh Internal energy, U Efficiency, η

Energy Total ∆E system has three macroscopic quantities: –∆KE: motion of system –∆PE: displacement of system in a gravitational field –∆U: Internal Energy is an extensive property.

Energy: Forms or Carriers Many forms: kinetic, potential, thermal, radiant, elastic, chemical etc…. Energy is [ex]changed (dynamic) and stored (static) It may be better to say energy is carried.

Work: Definition Means of energy transfer across a boundary: –Expansion work Wk = ΣF δx = F ∆x = F (x 2 – x 1 ) Wk = Σp A δx = = Σp δV = p ∆V –Shaft Work Wk = Σ T δ θ = T ∆ θ = T (θ 2 – θ 1 ) P V 1 2 dVdV P V 1 2 dVdV

Work: Sign Convention W>0: work transfer out of system W<0: work transfer into system

Caution! Work is path dependent dW = p∙dV meaningless because: ∫dW = W 2 – W 1 = ∫p ∙ dV Implies we can assign values to W 1 and W 2. Instead we write δW = p ∙ dV and W = ∫δW = ∫p ∙ dV Where δW is an inexact differential. i.e. the left side cannot be integrated and evaluated at the limits. Work is not a property.

Example: Work CO 2 is slowly heated from 50C to 500C in two steps as shown. –p 1 = 100 kPa –p 3 = 150 kPa –T 2 = 350C –m = 0.044kg Calculate total Work. P V 1 23 P 2 =P 3 P1P1 V3V3 V2V2 V1V1

Example: Work Assume quasi-equilibrium Assume Ideal gas P V 1 23 P 2 =P 3 P1P1 V3V3 V2V2 V1V1

Power Energy flow or energy current Power = dE/dt = I E Rate of doing Work Power = dW/dt = F ∙ dx/dt = F ∙ v W = ∫F ∙ v dt =∫p ∙ dV Involves a flow across a potential Power = -Δp |dV/dt| = -Δφ |dq/dt| = V∙I q

Heat: Definition Thermal energy moving across a boundary (not the lay definition) Only induced by a temperature difference Adiabatic process: no transfer of heat Like work, heat depends on the process, Heat is not a property Q>0: heat transfer to system Q<0: heat transfer from the system

Equivalence of Work and Heat Heat and work are both energy transitions Work can affect a system as if heat had been transferred. (the opposite is not always true)

Internal Energy In a Macroscopic analysis anything not KE or PE is Internal Energy, U. –Specific internal energy, u = U/m, is intensive. –Sensible U – related to temperature –Latent U – associated with phase change Microscopically Internal Energy is made of: –Translation, Rotation and Vibration of molecules –Chemical bonds within molecules –Plus: orbital states, nuclear spin and nuclear forces

Work in a Polytropic Process pV n = constant If n≠1, general polytropic process If n = 1, isothermal process If n = 0, isobaric process

Example: Polytropic Process A gas in a piston–cylinder assembly undergoes a process for which: pV n = constant P i = 3 bar, V i = 0.1 m 3, V f = 0.2 m 3 Determine the Work if a) n=1.5, b) n=1.0, c) n=0 p (bar) V (m 3 ) 1 2a 2b 2c pV n =k

Example: Polytropic Process, n=1.5 p (bar) V (m 3 ) 1 2a pV n =k

Example: Polytropic Process, n=1 p (bar) V (m 3 ) 1 2b pV n =k

Example: Polytropic Process, n=0 pV n =k p (bar) V (m 3 ) 1 2c

Reversibility Process are idealized as reversible –The process can be reversed with a return to the original state. –No dissipative effects –No production of entropy Irreversible work –Friction work and viscous work always oppose mechanical work –Transfer of heat through a finite ∆T